# lim of f(x,y)=frac{(x^{4}+4y^{2})}{(x^{2}+2y^{2})} at (0,0)

Functions
$$\displaystyle\lim$$ of $$\displaystyle{f{{\left({x},{y}\right)}}}={\frac{{{\left({x}^{{{4}}}+{4}{y}^{{{2}}}\right)}}}{{{\left({x}^{{{2}}}+{2}{y}^{{{2}}}\right)}}}}$$ at (0,0)

Now notice that $$\displaystyle{\frac{{{x}^{{{4}}}+{4}{y}^2}}{{{x}^{{{2}}}+{2}{y}^{{{2}}}}}}={\frac{{{x}^{{{2}}}+{4}{m}^{{{2}}}}}{{{1}+{2}{m}^{{{2}}}}}}\rightarrow{\frac{{{4}{m}^{{2}}}}{{{1}+{2}{m}^{{{2}}}}}}\ {a}{s}\ {x}\rightarrow{0}$$